Glad you liked Born Gold, it’s very easy to get into and like, and with a ~ x2 markup (~$40 retail or less), it’s a reasonable purchase for the meal, though not my personal favorite.
If you or anyone else can post a picture of their sake list, I can definitely recommend something from their lineup that might work. Bear in mind I have never eaten at N/naka (someday…someday…) but I can probably guess the flavor profile from the style and pictures of the food. Judging from their sample sake menu from the website, their sake offerings (particular Junmai Daiginjo) lean more towards aromatic type, off dry to semi dry to lighter flavors (Kun-shu types that are more fruit forward), and arguably some So-shu type sakes might work (light aroma and flavor, to go with more natural tasting simple light flavored food).
I’d be curious to find out what they do for sake pairing (and one can probably order one to share).